Each row of aerofoil members divides the duct into a series of sectoral passages, each bounded by the opposed suction and pressure surfaces of an adjacent pair of members and the radially inner and outer walls of the duct. The flow field within the sectoral passages is complex and includes a number of secondary vortical flows which are a major source of energy loss. Reference can be made to Sieverding (1985) "Secondary Flows in Straight and Annular Turbine Cascades", Thermodynamics and Fluids of Turbomachinery, NATO, Vol. 11, pp 621-624 for a detailed discussion of these flows. Their relative importance increases with increase of aerodynamic duty or decrease of aspect ratio. Not only is there energy dissipation in the secondary flows themselves, but they can also affect adversely the fluid flow downstream because they cause deviation of the exit angles of the flow from the row of aerofoil members.
It is found that it is the end wall boundary layers that give rise to a substantial part of these secondary flows. FIG. 1 shows a flow model illustration taken from Takeishi et al (1989), "An Experimental Study of the Heat Transfer and Film Cooling on Low Aspect Ratio Turbine Nozzles" ASME Paper 89-GT-187. This shows part of a row of turbine blades projecting from a cylindrical surface that forms a radially inner end wall of the annular passage into which the blade aerofoil extends. The principal flow features as shown in the model are:
(i) Rolling up of the inlet boundary layer L into a horseshoe vortex H at the blade leading edge due to the pressure variation at the intersection of the leading edge and the end wall. The pressure surface side leg of this flow becomes the core of a passage vortex P which is a dominant part of the secondary flow. On the end wall beneath the passage vortex a new boundary layer is formed, indicated as cross-flow B, which starts in the pressure side corner of the end wall of the blade passage. PA1 (ii) Upstream of the crossflow B the inlet boundary layer is deflected across the passage, as indicated by crossflow A. The end wall separation line S marks the furthest penetration of the bottom of the inlet boundary layer A into the blade passage and divides it from the new boundary layer (crossflow B) forming downstream of it. PA1 (iii) The new end wall boundary layer, crossflow B, continues onto the blade suction surface until it separates, along an aerofoil separation line V, and feeds into the passage vortex P. The horseshoe vortex suction side leg, referred to as the counter vortex U in the drawing, remains above the passage vortex P and moves away from the end wall as the passage vortex grows. PA1 (iv) A small corner vortex C may be initiated in the corner region between the blade suction surface and the end wall, rotating in the opposite sense to the passage vortex. PA1 (v) Also illustrated in FIG. 1 are the attachment line T which represents the division of the incoming boundary layer flow L between adjacent passages, and the saddle point D, where the attachment line T and the end wall separation line S intersect.
Typically, the passage vortex will increase the exit angle of the flow at the end wall (referred to as "over turning") with the compensatory reduction in exit angle away from the wall (referred to as "under turning"). These effects give rise to deviations of the inlet flow to the next aerofoil row, causing the angle of incidence of the flow on the aerofoils to vary positively or negatively from the design value and so reduce the aerodynamic efficiency of the flow.
There have been a number of proposals for reducing the secondary flows in the sectoral passages of a turbomachine, but with limited results. In recent work (Schnaus et al (1997), "Experimental and Numerical Investigation of the Influence of Endwall Inclination and Contouring on the Flow Field in a Highly Loaded Turbine Cascade" ISABE 97-7117, and Duden et al (1998), "Controlling the Secondary Flow in a Turbine Cascade 3D Airfoil Design and Endwall Contouring", ASME 98-GT-72), an axisymmetric profile was applied to the inclined end wall of a rotor blade in linear cascade which, unlike previous work did not change the inlet-to-exit passage area ratio. This profiling resulted in a small reduction in exit flow angle deviations and no change in loss. When combined with compound leaning and thickening of the aerofoil near the end wall, there was a significant reduction in secondary loss which, although counterbalanced by higher profile losses, still gave a significant reduction in exit angle deviations.
Non-axisymmetic end wall profiling has been attempted also. Atkins (1987), "Secondary Losses and End-wall Profiling in a Turbine Cascade" I Mech. E C255/87, pp29-42, describes two non-symmetric end wall profiles, both raised to one side, at the blade pressure surface or suction surface respectively but reducing to an unprofiled contour at the opposite blade surface, with the intention of reducing the maximum or minimum pressure on the relevant blade surface. Both profiles resulted in an overall increase in losses due to adverse effects on the flow near the profiled end wall causing separation and strong twisting of the blade wake. Morris et al (1975), "Secondary Loss Measurements in a Cascade of Turbine Blades with Meridional Wall Profiling", ASME 75-WA/GT-30 describes comparative tests of axisymmetric and non-axisymmetric profiles. In the non-axisymmetric case the contours were normal to a mid-passage streamline lying midway between the camber lines of the two blades bounding each blade passage, thereby raising the passage height over the entire width but with different chord-wise profiles. Although a better loss reduction was obtained at the unprofiled wall in the non-axisymmetric case, this advantage was cancelled by adverse effects close to the profiled wall and very strong twisting of the blade wake.